Definition

Be \(X_1, X_2, ...\) random variables with finite variances and be \(S_n = X_1+X_2+...+X_n\). The sequence \({X_n:n\geq1}\) satisfies the Law of Large Numbers if:

(Magalhães 2011)

http://vis.supstat.com/2013/04/law-of-large-numbers/

Uniform Distribution Example

Binomial Distribution Example

Exponential Distribution Example

Poisson Distribution Example

Cauchy Distribution Example

Definition

Be \({X_n:n\geq1}\) independent random variables, identically distributed and with expected value \(\mu\) and variance \(\sigma^2\), with \(0<\sigma^2<\infty\). For \(S_n=X_1+X_2+...+X_n\),

(Magalhães 2011)

https://www.youtube.com/watch?v=epq-dpMJIxs

Uniform Distribution Example

Binomial Distribution Example

Beta Distribution Example

Exponential Distribution Example